Incident radiation: Irradiance on the top of the snowpack can either be direct (i.e. uni-directional or "black-sky") or diffuse (i.e. isotropic or "white-sky").
Solar zenith angle: If the incident radiation is direct, users must specify the solar angle relative to the zenith direction.
Surface spectral irradiance conditions: The spectral distribution of incident radiation depends on the atmospheric state, including (e.g.,) cloudiness, gaseous composition, and surface pressure. The spectral irradiance distribution affects the broadband albedo but not spectral albedo. For example, clouds strongly absorb near-infrared radiation, leaving a higher proportion of surface irradiance as visible radiation, which snowpack tends to reflect strongly, thus producing higher broadband albedo. Seven characteristic atmospheric column options are currently provided. We derived the corresponding spectral profiles using an atmospheric radiative transfer model (Zender et al., 1997) with "standard" AFGL atmospheric profiles. Clear-sky conditions are assumed when direct incident radiation is selected, and cloudy-sky conditions are assumed when diffuse radiation is selected. Under cloudy conditions, the model plane-parallel cloud has an optical thickness of 10 (at 500 nm) and resides at 800 hPa, or in the lower-most atmospheric layer if the surface pressure is less than 800 hPa.
Snowpack thickness and density: The product of these two terms defines snowpack column mass (units of kg/m2), which is input to the radiative transfer model. Combinations of thickness and density that have an identical product produce identical albedo in the model.
Ice refractive index data: Libraries of Mie scattering properties were generated offline with four unique datasets of spectral ice refractive indices. Option (1) utilizes properties from Warren (1984) and Perovich and Govoni (1991), while option (2) utilizes the updated properties from Warren and Brandt (2008). Option (3) utilizes imaginary refractive indices from Picard et al. (2016) over the spectrum 320–600 nm, combined with absorption properties from Warren and Brandt (2008) at longer wavelengths and real refractive indices over the entire spectrum. The imaginary component over 200–320 nm is assumed constant and equal to the 320nm value from Picard et al (2016). Finally, option (4) applies refractive indices of carbon dioxide ice from Hansen (2005), as applied by Singh and Flanner (2016) to model the spectral albedo of Martian polar caps. Users will notice only slight differences in albedo between the different H2O refractive indices, but very distinctive changes with carbon dioxide ice.
Snow grain effective radius: This is the surface area-weighted mean radius of the collection of ice particles composing the snowpack. This property has strong influence on near-infrared reflectance and on the magnitude of albedo reduction caused by light-absorbing constituents. The resolution of input is 1 μm.
Snow grain shape: Users can select one of four distinct ice grain shapes. The parameterizations that account for ice particle asphericity are described by Fu (2007) and He et al. (2017). The primary impact of assuming non-spherical (more realistic) ice shapes is to reduce the scattering asymmetry parameter, which reduces the penetration depth of visible radiation and therefore reduces the impact of sub-surface light-absorbing constituents and underlying ground albedo, relative to spherical-grained snow (e.g., Libois et al., 2013; Dang et al., 2016). Users can see these effects when using the multi-layer offline version of SNICAR-ADv3.
Albedo of underlying ground: This parameter describes the solar broadband albedo of the surface underlying snowpack. The specified value is applied constantly across all spectral bands. Users can specify spectrally-varying ground albedo in the offline source code. Underlying ground albedo only influences reflectance of thin snowpack, but density and effective grain size also govern this influence.
Users can specify mass mixing ratios of two types of black carbon, two types of brown carbon, four types of dust particles residing in five particle size bins, one type of volcanic ash residing in five particle size bins, and snow algae composed of specified mass fractions of different light-absorbing pigments. We derive the optical properties for these light-absorbing constituents and ice grains with Mie solutions (Bohren and Huffman, 1983), using various indices of refraction and assumptions of particle size distributions as described below.
Black carbon: The black carbon optical properties are those used by Flanner et al. (2012), derived from spectrally-resolved refractive indices provided by Chang and Charalampopoulos (1990) and adjusted with a linear offset to achieve an imaginary component of 0.79 at 550nm, as recommended by Bond and Bergstrom (2006). We assume log-normal size distributions with a number-median radius of 40 nm, and geometric standard deviation of 1.8. The particle density is set to 1270 kg/m3 in order to achieve a mass absorption cross-section of about 7.5 m2/g at 550 nm, conforming with the central recommendation of Bond and Bergstrom (2006). The two types of black carbon that can be specified are uncoated (mimicking hydrophobic particles) and sulfate-coated (mimicking hydrophilic particles). The refractive sulfate coating has an outer radius 2.15 times larger than the uncoated black carbon and produces an absorption enhancement (per unit mass of black carbon) of about 1.5 (Bond et al., 2006). Various new and more sophisticated treatments of internally-mixed black carbon in ice have been explored (e.g., Flanner et al., 2012; Liou et al. 2011; He et al., 2017). All of these studies indicate that black carbon absorbs more solar energy, per unit mass, when embedded in weakly absorbing particles like ice, sulfate, or organics, with absorption enhancement factors typically ranging from 1–2. We therefore suggest using the sulfate-coated black carbon as a basic proxy for black carbon internally-mixed in any weakly-absorbing agent (ice, sulfate, etc), especially when precise knowledge of the particle/inclusion geometry is unknown.
Strongly-absorbing brown carbon: Two versions of "brown carbon" are also available, with identical size distributions and sulfate coatings as the black carbon species, but derived from imaginary refractive indices of Kirchstetter et al. (2004). These show very strong absorption at shorter (blue) wavelengths, rapidly tapering off to weak absorption in the red spectrum. The native data extend from 350–700 nm, and are extrapolated to 200 nm using a piecewise cubic hermite interpolating polynomial function. Data at wavelengths longer than 700 nm are linearly tapered down to a value of 10-5 at 5.0 μm. The real component of the refractive index is held constant at 1.53 and a particle density of 1270 kg/m3 is assumed. Organic aerosol species have been shown to have a huge range of absorptivity. The properties specified here are among the most absorptive of brown carbon measurements reported in the literature.
Mineral dust: Dust optical properties can depend strongly on the particle mineral composition and size distribution. The fraction of iron-containing minerals, in particular, has a strong impact on the absorptivity of dust. Four characteristic types of dust are available, each with unique sets of refractive indices. The Saharan dust is derived from dielectric mixing calculations assuming the "central hematite" mineralogical composition listed by Balkanski et al. (2007), which produced good agreement with AERONET measurements in regions strongly affected by Saharan dust. This is probably the most suitable option for "global-mean" dust. Dust properties from the San Juan Mountains, Colorado were determined from Mie inversions of measured spectral albedo of optically-thick dust samples (Skiles et al., 2017). Greenland dust properties are derived from dielectric mixing calculations of mineral refractive indices, based on measured elemental composition of Greenland dust samples, as described in the supplementary material of Polashenski et al. (2015). Finally, the Martian dust refractive indices were determined from spectral measurements from the Mars Reconnaissance Orbiter, as described by Wolff et al. (2009, 2010), and were utilized with SNICAR by Singh and Flanner (2016) to model the spectral albedo of Martian cryospheric surfaces. Mixing ratios within five particle size bins can be specified for each of these types of dust. The optical properties for each size class are determined with Mie calculation assuming a single lognormal size distribution with number median radius of 0.41μm and geometric standard deviation of 2.0, truncated at the diameter bounds indicated for each bin.
Volcanic ash: Volcanic ash mixing ratios can be specified in the same size bins available for mineral dust. The spectral refractive indices of ash are those developed for the "central forcing" scenario by Flanner et al., (2014, Figure 2) to model radiative impacts of the 2010 eruption of Eyjafjallajökull in Iceland. These properties were constrained by a variety of in-situ and sun photometer measurements of ash clouds from the eruption. This is currently the only type of volcanic ash available for use in the online version of SNICAR.
Snow algae: The representation of snow algae is based on techniques described by Cook et al. (2017). Here, the user specifies a number concentration of algal cells (cells/mL), the mean radius of the algae, and the dry cell mass fractions of four light-absorbing pigments. The pigment refractive index data originate from Dauchet et al. (2015). Optical properties for each allowable combination of pigment dry mass fraction and algal radius are derived offline using the Bruggeman approximation for dielectric mixing, followed by Mie calculations. The cellular volume fraction of water is fixed at 78%, with water refractive indices applied in the Bruggeman calculations. The portion of dry cellular matter not accounted for with pigments is assumed to be non-absorbing with a real refractive index of 1.5. The cell density is 1088 kg/m3, weighted with the density of water and an assumed dry matter density of 1400 kg/m3. The size distribution of algal cells is assumed to be Gaussian with a standard deviation of 10% of the mean radius.
This representation of snow algae should be viewed as experimental, with more work needed on the development and verification of techniques that accurately account for complexities such as cell geometry, presence of other pigments with unique spectral absorption profiles, and heterogeneity in the spatial positions of pigments and other cellular structures. Such work is ongoing.
Balkanski, Y., M. Schulz, T. Claquin, and S. Guibert (2007), Reevaluation of mineral aerosol radiative forcings suggests a better agreement with satellite and AERONET data, Atmos. Chem. Phys., 7 (1), 81-95, doi:10.5194/acp-7-81-2007.
Bohren, C. F., and D. R. Huffman (1983), Absorption and Scattering of Light by Small Particles, 530 pp., John Wiley & Sons, New York, NY.
Bond, T. C., and R. W. Bergstrom (2006), Light absorption by carbonaceous particles: An investigative review, Aerosol Sci. Technol., 40 (1), 27-67, doi: 10.1080/02786820500421521.
Bond, T. C., G. Habib, and R. W. Bergstrom (2006), Limitations in the enhancement of visible light absorption due to mixing state, J. Geophys. Res., 111, D20211, doi: 10.1029/2006JD00731.
Chang, H., and T. T. Charalampopoulos (1990), Determination of the wavelength dependence of refractive indices of flame soot, Proc. R. Soc. London, Ser. A, 430(1880), 577-591.
Cook, J. M., Hodson, A. J., Gardner, A. S., Flanner, M., Tedstone, A. J., Williamson, C., Irvine-Fynn, T. D. L., Nilsson, J., Bryant, R., and Tranter, M. (2017), Quantifying bioalbedo: a new physically based model and discussion of empirical methods for characterising biological influence on ice and snow albedo, The Cryosphere, 11, 2611-2632, doi: 10.5194/tc-11-2611-2017.
Cook, J. M., Tedstone, A. J., Williamson, C., McCutcheon, J., Hodson, A. J., Dayal, A., Skiles, M., Hofer, S., Bryant, R., McAree, O., McGonigle, A., Ryan, J., Anesio, A. M., Irvine-Fynn, T. D. L., Hubbard, A., Hanna, E., Flanner, M., Mayanna, S., Benning, L. G., van As, D., Yallop, M., McQuaid, J. B., Gribbin, T., and Tranter, M. (2020), Glacier algae accelerate melt rates on the south-western Greenland Ice Sheet, The Cryosphere, 14, 309-330, doi:10.5194/tc-14-309-2020.
Dang, C., Fu, Q., and Warren, S. (2016), Effect of Snow Grain Shape on Snow Albedo, J. Atmos. Sci., 73, 3573-3583, doi:10.1175/JAS-D-15-0276.1.
Dang, C., Zender, C. S., and Flanner, M. G. (2019), Intercomparison and improvement of two-stream shortwave radiative transfer schemes in Earth system models for a unified treatment of cryospheric surfaces, The Cryosphere, 13, 2325-2343, doi:10.5194/tc-13-2325-2019.
Dauchet, J., Blanco, S., Cornet, J.-F., and Fournier, R. (2015), Calculation of radiative properties of photosynthetic microorganisms, J. Quant. Spectrosc. Ra., 161, 60-84.
Dozier, J. and T. H. Painter (2004), Multispectral and hyperspectral remote sensing of alpine snow properties, Annu. Rev. Earth Planet. Sci., 32,465-494, doi: 10.1146/annurev.earth.32.101802.120404.
Flanner, M. G., Arnheim, J. B., Cook, J. M., Dang, C., He, C., Huang, X., Singh, D., Skiles, S. M., Whicker, C. A., and Zender, C. S. (2021), SNICAR-ADv3: a community tool for modeling spectral snow albedo, Geosci. Model Dev., 14, 7673-7704, https://doi.org/10.5194/gmd-14-7673-2021.
Flanner, M. G., C. S. Zender, J. T. Randerson, and P. J. Rasch (2007), Present day climate forcing and response from black carbon in snow, J. Geophys. Res., 112, D11202, doi:10.1029/2006JD008003.
Flanner, M. G., Liu, X., Zhou, C., Penner, J. E., and Jiao, C. (2012), Enhanced solar energy absorption by internally-mixed black carbon in snow grains, Atmos. Chem. Phys., 12, 4699-4721, doi:10.5194/acp-12-4699-2012.
Flanner, M. G., A. S. Gardner, S. Eckhardt, A. Stohl, J. Perket (2014), Aerosol radiative forcing from the 2010 Eyjafjallajökull volcanic eruptions, J. Geophys. Res. Atmos., 119, 9481-9491, doi:10.1002/2014JD021977.
Fu, Q. (2007), A new parameterization of an asymmetry factor of cirrus clouds for climate models, J. Atmos. Sci., 64, 4140-4150, doi: 10.1175/2007JAS2289.1.
Hansen, G. B. (2005), Ultraviolet to near-infrared absorption spectrum of carbon dioxide ice from 0.174 to 1.8 um, J. Geophys. Res., 110, E11003, doi:10.1029/2005JE002531.
He, C., Y. Takano, K.-N. Liou, et al. (2017), Impact of snow grain shape and black carbon-snow internal mixing on snow optical properties: Parameterizations for climate models, J. Climate, 30(24), 10019-10036, doi:10.1175/JCLI-D-17-0300.1.
Kokhanovsky, A. A., and Zege, E. P. (2004), Scattering optics of snow, Applied Optics, 43(7), 1589-1602, doi: 10.1364/AO.43.001589.
Kirchstetter, T. W., T. Novakov, and P. V. Hobbs (2004), Evidence that the spectral dependence of light absorption by aerosols is affected by organic carbon, J. Geophys. Res., 109, D21208, doi:10.1029/2004JD004999.
Libois, Q., G. Picard, J. France, L. Arnaud, M. Dumont , C. Carmagnola , and M. D. King (2013), Influence of grain shape on light penetration in snow, The Cryosphere, 7, 1803-1818, doi:10.5194/tc-7-1803-2013.
Liou, K. N., Takano, Y., and Yang, P. (2011), Light absorption and scattering by aggregates: Application to black carbon and snow grains, J. Quant. Spectrosc. Ra., 112, 1581-1594, doi:10.1016/j.jqsrt.2011.03.007.
Perovich, D. K., and J. W. Govoni (1991), Absorption coefficients of ice from 250 to 400 nm, Geophys. Res. Lett., 18, 1233-1235, doi:10.1029/91GL01642.
Picard, G., Libois, Q., and Arnaud, L. (2016), Refinement of the ice absorption spectrum in the visible using radiance profile measurements in Antarctic snow, The Cryosphere, 10, 2655-2672, doi:10.5194/tc-10-2655-2016.
Polashenski, C. M., J. E. Dibb, M. G. Flanner, J. Y. Chen, Z. R. Courville, A. M. Lai, J. J. Schauer, M. M. Shafer, and M. Bergin (2015), Neither dust nor black carbon causing apparent albedo decline in Greenland's dry snow zone: Implications for MODIS C5 surface reflectance, Geophys. Res. Lett., 42, 9319-9327, doi:10.1002/2015GL065912.
Singh, D., and M. G. Flanner (2016), An improved carbon dioxide snow spectral albedo model: Application to Martian conditions, J. Geophys. Res. Planets, 121, 2037-2054, doi:10.1002/2016JE005040.
Skiles, S. M., Painter, T., and Okin, G. (2017), A method to retrieve the spectral complex refractive index and single scattering optical properties of dust deposited in mountain snow, Journal of Glaciology. Vol. 63, 133-147, doi:10.1017/jog.2016.126.
Toon, O. B., C. P. McKay, T. P. Ackerman, and K. Santhanam (1989), Rapid calculation of radiative heating rates and photodissociation rates in inhomogeneous multiple scattering atmospheres, J. Geophys. Res., 94 (D13), 16,287-16,301.
Warren, S., and W. Wiscombe (1980), A model for the spectral albedo of snow. II: Snow containing atmospheric aerosols, J. Atmos. Sci., 37, 2734-2745.
Warren, S. G. (1984), Optical constants of ice from the ultraviolet to the microwave, Appl. Opt., 23, 1206-1225.
Warren, S. G., and R. E. Brandt (2008), Optical constants of ice from the ultraviolet to the microwave: A revised compilation, J. Geophys. Res., 113, D14220, doi:10.1029/2007JD009744.
Wiscombe, W. J., and S. G. Warren (1980), A model for the spectral albedo of snow. I: Pure snow, J. Atmos. Sci., 37, 2712-2733.
Wolff, M. J., M. D. Smith, R. T. Clancy, R. Arvidson, M. Kahre, F. Seelos IV, S. Murchie, and H. Savijarvi (2009), Wavelength dependence of dust aerosol single scattering albedo as observed by the Compact Reconnaissance Imaging Spectrometer, J. Geophys. Res., 114, E00D04, doi:10.1029/2009JE003350.
Wolff, M. J., R. T. Clancy, J. D. Goguen, M. C. Malin, and B. A. Cantor (2010), Ultraviolet dust aerosol properties as observed by MARCI, Icarus, 208(1), 143-155.
Zender, C. S., Brett Bush, Shelly K. Pope, Anthony Bucholtz, William D. Collins, Jeffrey T. Kiehl, Francisco P. J. Valero, and John Vitko, Jr. (1997), Atmospheric absorption during the Atmospheric Radiation Measurement (ARM) Enhanced Shortwave Experiment (ARESE), J. Geophys. Res., 102(D25), 29901-29915.